pythonterm3.ipynb

{
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3 style=\"color:red;text-align:center;\">Python pour le programme de Terminale\n",
    "</h3>\n",
    "<p><br></p>\n",
    "<div style=\"text-align:justify;\">\n",
    "\n",
    "<ol>\n",
    "    <li style=\"padding-bottom:1em;\"><a href=\"./pythonterm.ipynb\" > La bibliothèque random </a></li>\n",
    "    <li style=\"padding-bottom:1em;\"><a href=\"./pythonterm2.ipynb\" > Simuler un processus aléatoire illustrant la détermination de la valeur d’une grandeur avec incertitudes types composées </a></li>\n",
    "    <li style=\"padding-bottom:1em;\"><a href=\"./pythonterm3.ipynb\" > Représenter, à l’aide d’un langage de programmation, l’évolution des quantités de matière des espèces en fonction du volume de solution titrante versé </a></li>\n",
    "    <li style=\"padding-bottom:1em;\"><a href=\"./pythonterm4.ipynb\" > Déterminer, à l’aide d’un langage de programmation, le taux d’avancement final d’une transformation, modélisée par la réaction d’un acide sur l’eau </a></li>\n",
    "    <li style=\"padding-bottom:1em;\"><a href=\"./pythonterm5.ipynb\" > Tracer, à l’aide d’un langage de programmation, le diagramme de distribution des espèces d’un couple acide-base de pKa donné </a></li>\n",
    "    <li style=\"padding-bottom:1em;\"><a href=\"./pythonterm6.ipynb\" > À l’aide d’un langage de programmation et à partir de données expérimentales, tracer l’évolution temporelle d’une concentration, d’une vitesse volumique d’apparition ou de disparition et tester une relation donnée entre la vitesse volumique de disparition et la concentration d’un réactif </a></li>\n",
    "    <li style=\"padding-bottom:1em;\"><a href=\"./pythonterm7.ipynb\" > Exploiter, à l’aide d’un langage de programmation, des données astronomiques ou satellitaires pour tester les deuxième et troisième lois de Kepler </a></li>\n",
    "</ol></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1 style=\"text-align:center;\">3. Représenter, à l’aide d’un langage de programmation, l’évolution des quantités de matière des espèces en fonction du volume de solution titrante versé </h1>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Comme pour le tableau d'avancement, nous allons travailler avec un pas dV petit devant le volume total versé. On limitera le volume versé à 25 mL, volume d'une burette graduée.\n",
    "\n",
    "Le volume à l'équivalence $V_{eq}$ a été mesuré expérimentalement.\n",
    "\n",
    "L'exemple choisi ici est le titrage directe du diiode $I_2$ par le thiosulfate $S_2O_3^{2-}$.\n",
    "\n",
    "\n",
    "|     | $I_2$ |  +  | $2\\ S_2O_3^{2-}$ | $\\longrightarrow$ | $2\\ I^-$ |  +  | $S_4O_6^{2-}$ |\n",
    "|:---:|:-----:|:---:|:----------------:|:---:|:-------:|:---:|:------------:|\n",
    "| EInit | $C_1 V_1$ |  |  $C_2 V_{versé}$ |  |  $0$  |   |  $0$  |\n",
    "| EInter | $C_1 V_1 - x$ |  |  $C_2 V_{versé} - 2 x$ |  |  $2 x$ |   | $x$ |\n",
    "| EF | $C_1  V_1 - x_f$  |  |  $C_2 V_{versé} - 2 x_f$ |  | $2 x_f$ |  |  $x_f$ |\n",
    "\n",
    "$$ \\ $$\n",
    "Afin de déterminer $x_f$, il faut déterminer le réactif limitant. Le réactif limitant est celui pour lequel la quantité de matière à l'état final arrive à zéro en premier. L'avancement $x_f$ que l'on va utiliser est donc la valeur la plus petite entre $C_1 V_1$ et $\\frac{C_2 V_{versé}}{2}$ ici."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Données\n",
    "V1 = 10e-3 # L\n",
    "C2 = 1e-2 # mol/L\n",
    "\n",
    "Veq = 12.0e-3 # L\n",
    "C1 = C2*Veq / (2*V1)\n",
    "\n",
    "V2 = [0] # On initialise avec un volume versé nul\n",
    "dV = 1e-5 # L\n",
    "\n",
    "# Premier point: Etat final avec Vversé = 0\n",
    "n1 = [C1*V1] # I2\n",
    "n2 = [0] # thiosulfate\n",
    "n3 = [0] # I-\n",
    "n4 = [0] # tetrathionate\n",
    "\n",
    "while V2[-1] < 25e-3: # On limite à 25 mL\n",
    "    V2.append(V2[-1] + dV)\n",
    "    xf = min(C1*V1,0.5*C2*V2[-1]) # calcul de xf pour le V2 considéré\n",
    "    n1.append(C1*V1-xf)\n",
    "    n2.append(C2*V2[-1]-2*xf)\n",
    "    n3.append(2*xf)\n",
    "    n4.append(xf)\n",
    "    \n",
    "\n",
    "plt.plot(V2,n1,label=r\"$n_{I_2}$\")\n",
    "plt.plot(V2,n2,label=r\"$n_{S_2O_3^{2-}}$\")\n",
    "plt.plot(V2,n3,label=r\"$n_{I^{-}}$\")\n",
    "plt.plot(V2,n4,label=r\"$n_{S_4O_6^{2-}}$\")\n",
    "plt.legend()\n",
    "plt.xlabel(\"Volume versé (L)\")\n",
    "plt.ylabel(\"Quantité de matière (mol)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Une autre façon de voir les choses est de séparer le comportement en 2 cas, avant ou après équivalence. Le résultat est bien entendu le même.\n",
    "\n",
    "$$ \\ $$\n",
    "<div style=\"text-align: center; font-weight: bold\">Avant équivalence  </div>\n",
    "\n",
    "|     | $I_2$ |  +  | $2\\ S_2O_3^{2-}$ | $\\longrightarrow$ | $2\\ I^-$ |  +  | $S_4O_6^{2-}$ |\n",
    "|:---:|:-----:|:---:|:----------------:| :---: | :-------: | :---: | :------------: |\n",
    "| EInit | $C_1 V_1$ |  |  $C_2 V_{versé}$ |  |  $0$  |   |  $0$  |\n",
    "| EInter | $C_1 V_1 - x$ |  |  $C_2 V_{versé} - 2 x$ |  |  $2 x$ |   | $x$ |\n",
    "| EF | $C_1  V_1 - x_f = C_1 V_1 - \\frac{ C_2 V_{versé}}{2}$  |  |  $C_2 V_{versé} - 2 x_f = 0$ |  | $2 x_f = C_2 V_{versé}$ |  |  $x_f = \\frac{C_2 V_{versé}}{2} $ |\n",
    "\n",
    "  \n",
    "$$ \\ $$\n",
    "<div style=\"text-align: center; font-weight: bold\">Après équivalence  </div>\n",
    "\n",
    "|     | $I_2$ |  +  | $2\\ S_2O_3^{2-}$ | $\\longrightarrow$ | $2\\ I^-$ |  +  | $S_4O_6^{2-}$ |\n",
    "|:---:|:-----:|:---:|:----------------:|:---:|:-------:|:---:|:------------:|\n",
    "| EInit | $C_1 V_1$ |  |  $C_2 V_{versé}$ |  |  $0$  |   |  $0$  |\n",
    "| EInter | $C_1 V_1 - x$ |  |  $C_2 V_{versé} - 2 x$ |  |  $2 x$ |   | $x$ |\n",
    "| EF | $C_1  V_1 - x_f = 0$  |  |  $C_2 V_{versé} - 2 x_f = C_2 V_{versé} - 2 C_1 V_1$ |  | $2 x_f = 2 C_1 V_1$ |  |  $x_f = C_1 V_1$ |\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Données\n",
    "V1 = 10e-3 # L\n",
    "C2 = 1e-2 # mol/L\n",
    "\n",
    "Veq = 12.0e-3 # L\n",
    "\n",
    "V2 = [0] # On initialise avec un volume versé nul\n",
    "dV = 1e-5 # L\n",
    "\n",
    "# Premier point: Etat final avec Vversé = 0\n",
    "n1 = [C1*V1] # I2\n",
    "n2 = [0] # thiosulfate\n",
    "n3 = [0] # I-\n",
    "n4 = [0] # tetrathionate\n",
    "\n",
    "while V2[-1] < 25e-3:\n",
    "    V2.append(V2[-1] + dV)\n",
    "    if V2[-1] <= Veq: # Avant équivalence\n",
    "        n1.append(C1*V1-0.5*C2*V2[-1])\n",
    "        n2.append(0)\n",
    "        n3.append(C2*V2[-1])\n",
    "        n4.append(0.5*C2*V2[-1])\n",
    "    else: # Après équivalence\n",
    "        n1.append(0)\n",
    "        n2.append(C2*V2[-1] - 2*C1*V1)\n",
    "        n3.append(2*C1*V1)\n",
    "        n4.append(C1*V1)\n",
    "    \n",
    "\n",
    "plt.plot(V2,n1,label=r\"$n_{I_2}$\")\n",
    "plt.plot(V2,n2,label=r\"$n_{S_2O_3^{2-}}$\")\n",
    "plt.plot(V2,n3,label=r\"$n_{I^{-}}$\")\n",
    "plt.plot(V2,n4,label=r\"$n_{S_4O_6^{2-}}$\")\n",
    "\n",
    "plt.legend()\n",
    "plt.xlabel(\"Volume versé (L)\")\n",
    "plt.ylabel(\"Quantité de matière (mol)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercice\n",
    "1. En adaptant les codes proposés dans les exemples ci-dessus, représenter l’évolution des quantités de matière des espèces en fonction du volume de solution titrante versé dans le cas du titrage direct de la soude par l'acide chlorhydrique. L'acide chlorhydrique a une concentration de $1,00 \\cdot 10^{-2}\\ mol.L^{-1}$, le volume de soude titré est de $V_1 = 10,0\\ mL$ et le volume équivalent est de $V_{eq} = 11,2\\ mL$\n",
    "2. Même question pour le titrage dont la réaction support est $MnO_{4\\ (aq)}^{-} + 5 Fe_{\\ \\ (aq)}^{2+} + 8 H_{\\ \\ (aq)}^{+} \\longrightarrow Mn_{\\ \\ (aq)}^{2+} + 5 Fe_{\\ \\ (aq)}^{3+} + 4 H_2O_{\\ \\ (l)}$. Ce sont les ions fer II qui sont dosés. Le volume de solution d'ions $Fe^{2+}$ prélevé est de $V_1 = 20,0\\ mL$. La solution de permanganate de potassium utilisée a une concentration $C_2 = 5,0 \\cdot 10^{-3}\\ mol.L^{-1}$. Le volume équivalent est mesuré à $V_E = 9,5\\ mL$.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 1.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 2.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p style=\"text-align:justify;\"><span style=\"float:left;\"><a href=\"./pythonterm2.ipynb\" > page précédente </a></span> <span style=\"float:right;\"><a href=\"./pythonterm4.ipynb\" > page suivante </a></span></p>\n"
   ]
  }
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